Nicholson's blowflies equation and a delay independent Aizerman problem * *The research has been supported by the Project CNCS-ROMANIA PN-II-ID-PCE-3-0198.

2013 ◽  
Vol 46 (3) ◽  
pp. 238-241
Author(s):  
Vladimir Rasvan
Keyword(s):  
Nicholson’S Blowflies Equation ◽  
Aizerman Problem

Stability and Hopf bifurcation analysis for Nicholson's blowflies equation with non-local delay

2012 ◽  
Vol 23 (6) ◽  
pp. 777-796 ◽  
Author(s):  
RUI HU ◽  
YUAN YUAN
Keyword(s):  
Hopf Bifurcation ◽  
Upper And Lower Solutions ◽  
Laboratory Data ◽  
Steady State Solution ◽  
Steady States ◽  
Nicholson’S Blowflies Equation ◽  
Non Local ◽  
The Stability ◽  
Manifold Theory ◽  
Theoretical Results

We consider a diffusive Nicholson's blowflies equation with non-local delay and study the stability of the uniform steady states and the possible Hopf bifurcation. By using the upper- and lower solutions method, the global stability of constant steady states is obtained. We also discuss the local stability via analysis of the characteristic equation. Moreover, for a special kernel, the occurrence of Hopf bifurcation near the steady state solution and the stability of bifurcated periodic solutions are given via the centre manifold theory. Based on laboratory data and our theoretical results, we address the influence of various types of vaccinations in controlling the outbreak of blowflies.

On the Aizerman problem

2009 ◽  
Vol 70 (7) ◽  
pp. 1120-1131 ◽  
Author(s):  
G. A. Leonov
Keyword(s):  
Aizerman Problem

scholarly journals Dynamics of the diffusive Nicholson's blowflies equation with distributed delay

2000 ◽  
Vol 130 (6) ◽  
pp. 1275-1291 ◽  
Author(s):  
S. A. Gourley ◽  
S. Ruan
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Comparison Principle ◽  
Distributed Delay ◽  
Energy Methods ◽  
Integral Convolution ◽  
Nicholson’S Blowflies Equation ◽  
Uniform State ◽  
Linearized Stability ◽  
Uniform Steady State

In this paper we study the diffusive Nicholson's blowflies equation. Generalizing previous works, we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible. The linearized stability of the non-zero uniform steady state is studied in detail, mainly by using the principle of the argument. Global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations. Finally, we consider what bifurcations are possible from the non-zero uniform state in the case when it is unstable.

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